Wednesday, December 13, 2023 - 14:15 in V3-201 + Zoom
Controlling a generalized Fokker-Planck equation via inputs with nonlocal action
A talk in the Bielefeld Stochastic Afternoon series by
Stefana Anita
| Abstract: |
This paper concerns an optimal control problem (P) related to a
generalized Fokker-Planck equation. Basic properties of the solutions to the generalized FP equation are
derived via a semigroup approach in the space $H^{−1}(\mathbb{R}^d)$. Problem (P) is proven to be deeply related to a
stochastic optimal control problem (PS) for a McKean-Vlasov equation. The existence of an optimal control is
obtained for the deterministic problem (P). The existence of an optimal control is established for an
approximating optimal control problem (Ph) related to a backward Euler approximation of the generalized FP
equation (with a constant discretization step h). One proves under additional hypotheses that “(Ph) converges
to (P)” in a certain sense. First-order necessary conditions for (Ph) are derived as well.
Within the CRC this talk is associated to the project(s): A5 |
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